New results on the robust stability of PID controllers with gain and phase margins for UFOPTD processes. (March 2016)

• Record Type: Journal Article
• Authors: Jin, Q.B.; Liu, Q.; Huang, B.
• Is Part Of: ISA transactions. Volume 61(2016:Mar.)
• Page Start: 240
• Page End: 250
• Publication Date: 2016-03
• Subjects: UFOPTD processes -- PID control -- Phase margin -- Gain margin; Engineering instruments -- Periodicals; Engineering instruments; Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.isatra.2015.11.028
• Languages: English
• ISSNs: 0019-0578

Abstract

Abstract: This paper considers the problem of determining all the robust PID (proportional–integral–derivative) controllers in terms of the gain and phase margins (GPM) for open-loop unstable first order plus time delay (UFOPTD) processes. It is the first time that the feasible ranges of the GPM specifications provided by a PID controller are given for UFOPTD processes. A gain and phase margin tester is used to modify the original model, and the ranges of the margin specifications are derived such that the modified model can be stabilized by a stabilizing PID controller based on Hermite–Biehlers Theorem. Furthermore, we obtain all the controllers satisfying a given margin specification. Simulation studies show how to use the results to design a robust PID controller. Abstract : Highlights: The range of GPM that a PID controller can provide for an UFOPTD model is given. All the admissible PID parameters satisfying a given margin specification are computed. A graphic method to design the robust PID controller is proposed.